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What is Fermat’s Last Theorem?
Fermat’s Last Theorem is a conjecture by Pierre de Fermat that states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2. The theorem has been proven for all n values up to 4,000,000, but remains unproven for all n values greater than that.
Equation of the Last Theorem Stated by Fermat
The equation of the last theorem stated by Fermat is xn + yn = zn for positive integers x, y, and z. This theorem states that for a positive integer n, the equation xn + yn = zn has no positive integer solutions for x, y, and z when n is greater than 2.
Fermat’s Last Theorem Proof Simplified
Fermat’s Last Theorem states that for any natural number n, there is no positive integer x such that xn + yn = zn where n is greater than 2.
Proof:
Assume that there is a positive integer x such that xn + yn = zn where n is greater than 2. This would mean that there is a positive integer k such that xk + yk = zk.
But then,
xk + yk = zk
xk – yk = 0
This means that x and y are both zero, which is a contradiction because x and y cannot be both zero and positive integers at the same time.
Hence, there is no positive integer x such that xn + yn = zn where n is greater than 2.
Final Thoughts
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For more visit Superposition Theorem and How does it Work
